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JEE Main Math Class 11 Complex Numbers and Quadratic Equations Part 2 Questions
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© examsnet.com
Question : 95
Total: 100
If
α
and
β
are the roots of the quadratic equation,
x
2
+
x
sin
θ
−
2
sin
θ
=
00
,
θ
∈
(
0
,
π
2
)
,
then
α
12
+
β
12
(
α
−
12
+
β
−
12
)
(
α
−
β
)
24
is equal to :
[April 10, 2019 (I)]
2
12
(
sin
θ
−
4
)
12
2
12
(
sin
θ
+
8
)
12
2
12
(
sin
θ
−
8
)
6
2
6
(
sin
θ
+
8
)
12
Validate
Solution:
Given equation is,
x
2
+
x
sin
θ
−
2
sin
θ
=
0
α
+
β
=
−
sin
θ
and
α
β
=
−
2
sin
θ
(
α
12
+
β
12
)
α
12
β
12
(
α
12
+
β
12
)
(
α
−
β
)
24
=
(
α
β
)
12
(
α
−
β
)
24
∴
|
α
−
β
|
=
√
(
α
+
β
)
2
−
4
α
β
=
√
sin
2
θ
+
8
sin
θ
∴
(
α
β
)
12
(
α
−
β
)
24
=
(
2
sin
θ
)
12
sin
12
θ
(
sin
θ
+
8
)
12
=
2
12
(
sin
θ
+
8
)
12
© examsnet.com
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